For a given input value $m$, the function $g$ outputs a value $n$ to satisfy the following equation. $-2m-5n=7m-3n$ Write a formula for $g(m)$ in terms of $m$. $g(m)=$
Solution: $g(m)$ expresses $n$ as a function of $m$. To arrive at a correct formula, all we have to do is solve the equation for $n$. $ \begin{aligned}-2m-5n&=7m-3n\\\\ -2n&=9m\\\\ n&=\dfrac{9m}{-2}\end{aligned}$ Therefore, this formula expresses $n$ as a function of $m$ : $ g(m)=-\dfrac{9}{2}m$